**Feed:** Dr. Myron Evans

**Posted on:** Tuesday, July 12, 2011 5:43 AM

**Author:** metric345

**Subject:** Note on the Complementary Function

This is a clear example taken from Stephenson.”Mathematical Methods for Science Students”. The new metric m(r, t) is the complementary function, which is the solution to the reduced equation. The complete solution is the solution of the original constraint equation is the particular integral obtained by Horst using computer algebra. I chose the particular integral to be a very large negative constant (approaching negative infinity) so m sub p vanishes. In this example, eq. (3) is not a solution of eq. (1). This has been checked again by Dr Horst Eckardt using computer algebra. For an example of this method see Marion and Thornton pp. 114 ff. in the well known context of Euler resonance. Transient effects are described by the complementary function, and resonance by the particular integral. So having carried out this final check I think that all is fine. The complete solution is therefore:
m = m sub p + m sub c where m sub p = 0 So the new general metric is a kind of fall transient which behaves much better than SM (graphs just sent over by HE). |